Work/Energy Conservation Problem w/ Initial Velocity

In summary, the problem involves an object with a mass of 0.50kg and an initial speed of 2.00 m/s subjected to an applied force of 10.0N on a floor with a coefficient of friction of 0.40. The goal is to determine the object's speed at a distance of 15.0m using the general energy conservation formula. After solving, the answer obtained is 22.1 m/s, but the correct answer is 2.21 m/s, indicating a possible error in the solution key.
  • #1
Bread Boy
6
0

Homework Statement


An applied force of 10.0N acts horizontally on a 0.50kg mass on a floor with the coefficient of friction being 0.40. If the object had an initial speed of 2.00 m/s, determine its speed at 15.0m.


Homework Equations


General Energy Conservation Formula
Ek(i) + Ep (i) + Einput(i) = Ek(f) + Ep(f) + Eoutput(f)


The Attempt at a Solution


1/2 * 0.5 * 2^2 + (10 * 15) = 1/2 * 0.5 * v^2 + ((0.4)(0.5)(9.8) * 15)
(hope I wrote it down correctly haha)
v = 22.1 m/s

Now I know the answer is supposed to be 2.21 m/s, but I have no idea how I ended up with what seems to be a decimal place in the wrong position. What gives?

Thanks in advance for the help!
 
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  • #2
Your work--and your answer--looks fine to me.
 
  • #3
So I was correct? The solution key must have been wrong then. Thanks a bunch!
 

FAQ: Work/Energy Conservation Problem w/ Initial Velocity

How do you calculate the initial velocity in a work/energy conservation problem?

To calculate the initial velocity in a work/energy conservation problem, you can use the formula: KEi + PEi = KEf + PEf, where KE represents kinetic energy and PE represents potential energy. Make sure to use the correct units for energy (Joules) and mass (kilograms).

What is the conservation of energy principle in a work/energy conservation problem?

The conservation of energy principle states that energy cannot be created or destroyed, only transferred or converted from one form to another. In a work/energy conservation problem, the initial energy of the system (KEi + PEi) must equal the final energy of the system (KEf + PEf).

Can the initial velocity be negative in a work/energy conservation problem?

Yes, the initial velocity can be negative in a work/energy conservation problem. A negative initial velocity indicates that the object is moving in the opposite direction of the chosen positive direction. However, when calculating the final velocity, make sure to use the correct sign convention to determine the direction of the final velocity.

What is the significance of solving for the initial velocity in a work/energy conservation problem?

Solving for the initial velocity in a work/energy conservation problem allows you to determine the starting velocity of an object in a given scenario. This information can be useful in understanding the motion and behavior of the object, as well as predicting its future position and velocity.

Can the initial velocity affect the final velocity in a work/energy conservation problem?

Yes, the initial velocity can affect the final velocity in a work/energy conservation problem. The initial velocity is one of the factors that contribute to the total initial energy of the system. If the initial velocity is increased, the initial energy will also increase, resulting in a higher final velocity. Similarly, a decrease in initial velocity will lead to a lower final velocity.

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